MID TERM EXAM 1 WEEK FROM TODAY

http://www.homepage.montana.edu/~kmw/

Today

Fluvial Process– Geomorphic Work– Bankfull discharge – Hydraulic geometry – Open channel toolbox

Channel Morphology = f(River Work)

• Work = Force x distance• Power = Rate at which work is done• Stream Power: one way to measure

entrainment and transport of bedload • The work done by a river is estimated

by – the amount of sediment it transports during

any given flood– “the conditions under which rivers adjust or

maintain their morphology”

gQS

Geomorphic Work:Frequency and Magnitude

Transports the most sediment

Elf?Man?Giant?

from Wolman and Miller (1960)

ALLUVIAL RIVERS ARE THE AUTHORS OF THEIR OWN GEOMETRY

• Given enough time, rivers construct their own channels.

• A river channel is characterized in terms of its bankfull geometry.

• Bankfull geometry is defined in terms of river width and average depth at bankfull discharge.

• Bankfull discharge is the flow discharge when the river is just about to spill onto its floodplain.

Text by Peter Wilcock/Johns Hopkins Univ.

CAVEAT: NOT ALL RIVERS HAVE A DEFINABLE BANKFULL GEOMETRY!

Rivers in bedrock often have no active floodplain, and thus no definable bankfull geometry.

Highly disturbed alluvial rivers are often undergoing rapid downcutting. What used to be the floodplain becomes a terrace that is almost never flooded. Time is required for the river to construct a new equilibrium channel and floodplain.

Wilson Creek, Kentucky: a bedrock stream. Image courtesy A. Parola.

Reach of the East Prairie Creek, Alberta, Canada undergoing rapid

downcutting due to stream straightening. Image courtesy D. Andres.

THRESHOLD CHANNELS

Trinity Dam on the Trinity River, California, USA. A threshold channel forms

immediately downstream.

Threshold gravel-bed channels are channels which are barely not able to move the gravel on their beds, even during high flows. These channels form e.g. immediately downstream of dams, where their sediment supply is cut off. They also often form in urban settings, where paving and revetment have cut off the supply of sediment. Threshold channels are not the authors of their own geometry.

Adjustments in the Fluvial System

Hydraulic Geometry

• Q = Vel x Cross-sectional flow area= Vel x width x depthWhich of these 3 variables changes most to

accommodate more Q, either downstream or at a given location?

• Relationships between width, depth, and velocity and discharge

• Describes how w, d, v increase with discharge

Hydraulic Geometry

1

1

mfb

kca

kQcQaQvdwQ

gQs

kQv

cQd

aQw

mfb

z

m

f

b(Leopold and Maddock, 1953)

At-a-Station and Downstream Hydraulic Geometry

34.

4.

26.

kQv

cQd

aQw

1.

4.

5.

kQv

cQd

aQw

at-a-station downstream

Downstream hydraulicgeometry relations(Leopold and Maddock,1953)

Used Q = Mean annual flow (MAF)

At-a-station hydraulicgeometry relations(Leopold and Maddock,1953)

Downstream hydraulic geom. relationscompared for 8 river systems

Rate of increase of w, d and v is similar regardless of river size!

Leopold and Maddock, 1953

Fonstad and Marcus, 2003

On Soda Butte Creek, measuring bankfull width

Adjustments in the Fluvial System

Lane’s balance: Model of the channel adjustment to water

and sediment loads• Qs d50 ~ Qw S

– Qs = sediment discharge (kg/s)

– Qw = water discharge (cm/s)

– d50 = sediment size (m)– S = slope (m/m)

Gilbert’s Fluvial Process• Joined John Wesley Powell survey in Utah, 1874

• First coined the concept of “graded streams”

• A stream’s form is defined by its ability to transport load, and that a “graded” stream condition will exist when the stream can just carry the load supplied to it– “The transportation of debris by running water”, USGS Prof. Paper

86, Gilbert, 1914

• Crux of this hypothesis was that mechanical forces act against rock to create form

“If a stream which is loaded to its full capacityreaches a point where the slope is less, it becomes overloaded and part of the load is dropped,making a deposit.”

“If the slope of a stream’s bed is not adjusted to thestream’s discharge and to the load it has to carry,then the stream continues to erode or deposit, or bothuntil an adjustment has been effected and the slope isjust adequate for the work”

“If a fully loaded stream reaches a point where the slope is steeper, its enlarged capacity causesit to take more load, and taking of load erodes the bed.”

Graphic by Peter WilcockText by G.K. Gilbert, “HydraulicMining Debris in the Sierra Nevada”USGS Prof. Paper 105, 1917.

Ex. of Lane’s balance

• Mine discharges large quantities of fine grained sediment (<d50) into river– River response?

• Madison slide occurs and deposits large mass of of cobble/boulder (>d50)– River response?– Complex response?

Deposition

Example of process linkage and complex response

1959 Hebgen Lake earthquake-inducedlandslide

t0, x0

Deposition t2, x3Incision t2, x2

Incision t3, x3Locke, 1998

Deposition t3, x4

TIM

E t1, x1Incision t1, x2

SPACE

The Open-Channel Toolbox TM Peter Wilcock

• Conservation Relations– Conservation of Mass

(Continuity)– Conservation of

Energy– Conservation of

Momentum

• Constitutive Relations– Flow Resistance– Sediment Transport

Conservation of Mass (Continuity)

• Mass is neither created nor destroyed

• Inputs = outputs• Inputs and outputs for

fluid flow are discharge– Vel x Flow Area

U1A1 = U2A2

Conservation of Momentum (Force-balance)

• Newton’s Second Law

• In steady, uniform flow,

• Depth-slope product

0F

maF

PLALg o sin

gRS

Unsteady, nonuniform flow

• Flow accelerates in space and time

1-d St. Venant eqn.

Rearranged 1-d St. Venant eqn.

Potential Energy and Kinetic Energy

• Bernoulli energy equation– H = d + Z + V2/2g + losses– d = depth– Z = elevation above datum,

e.g. sea level– V = velocity of flow– g = gravity

H1

H1

• Energy is neither created nor destroyed• Two components

– kinetic ( )– potential (z+h)

• Energy is also converted to heat, hf

• H1 =H2 + hf

Conservation of Energy

g

U

2

2

http://ga.water.usgs.gov/edu/hyhowworks.html

Flow Resistance

• Relation between velocity, flow depth, basal shear stress, and hydraulic roughness

• A variety of relations exist including– Manning’s– Chezy

• Empirical• The big unknown: n

n

RSU

32

Using continuity,

ARn

SUAQ 3

2

(Metric)Multiply by 1.49 for English units

• Chezy

– V= C√RS

– Where

• C=Chezy roughness (22-220)

• V= velocity

• R=hydraulic radius

• S=channel slope

• Manning

– V=(1.49/n) R2/3 S1/2

– Where

• n = Manning’s roughness coefficient (0.02-006)

Flow Resistance Eqns.

LWD covering less than 2% of the streambed can provide half

the total roughness or flow resistance. This results in a finer

streambed substrate.

Buffington and Montgomery 1999, WRR 36, 3507-3521Manga and Kirchner, 2000, WRR 36, 2373-2379.